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Links 1 through 10 of 212 by Chad Orzel tagged math

Different browsers do this differently. Some show a little bar to indicate how much of the file you have downloaded as well as an estimate of how much longer you can expect to wait. Well, now the time has come. I am going to check these download progress bars. Why? I have no idea.

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Science fiction writers can make use of worm holes or warp drives to overcome this restriction, but it is not clear that such things can ever be made to work in reality.  Another way to get around the problem may be to use the relativistic effects of time dilation and length contraction to cover large distances within a reasonable time span for those aboard a space ship.  If a rocket accelerates at 1g (9.81 m/s2) the crew will experience the equivalent of a gravitational field with the same strength as that on Earth.  If this could be maintained for long enough they would eventually receive the benefits of the relativistic effects which improve the effective rate of travel.

What then, are the appropriate equations for the relativistic rocket?

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A collection of classic estimation problems, with answers, written by E.M. Purcell for the American Journal of Physics back in the day.

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Consider a square with an area of 24. The side has length √24.

This square can be divided into 4 smaller squares, each with an area of 6. The sides of these smaller squares have length √6. Two of these lengths make up the side length of the large square, so √24 = 2√6.

24 can also be divided into 3 rectangles, each with an area of 8. Again, correct, but not helpful. How to simplify √45 as 3√5 and √72 as 6√2 are also shown above. Again, factors that are perfect squares are key.

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I am not typically interested in lotteries.  They seem silly and I am seriously beginning to question their usefulness in bringing about a good harvest.  But this morning I read in the news that the Mega Millions lottery currently has a world record jackpot up for grabs.  In fact, the jackpot is so big...

Tonight Show Audience:  HOW BIG IS IT?

It is so big that I decided to do a little bit of analysis on the expected returns.  Zing!

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Since its digits are random, and they never end, in principle any sequence you could ever imagine should show up in pi eventually.  In fact there is a nifty website here that will let you search for arbitrary strings (using a 5-bit format) in first 4 billion digits, for example "alemi" seems to show up at around digit 3149096356.

So in principle, I could send you just an index, and a length, and you could compute the resulting file.

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Benford's law states that real-world numbers start more often with a 1 than a 2, more often with 2 than 3 and so on. If your dataset does not follow this distribution, it might hint at human interference.

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This video shows why humans are terrible at generating random sequences. Why flipping a coin is different & introduces the concept of frequency stability

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I’m convinced that the Standards for Mathematical Practice are doomed to fail in most schools.

Why? Because it seems that most teachers and principals don’t understand a simple fact: to teach elementary school math well, you have to know elementary school math really well. And most people (be they teachers, principals or otherwise) simply don’t understand much elementary school math.

I don’t know what teacher preparation programs are doing out there when it comes to math instruction, but from my experience in hiring teachers and my stint as an adjunct in one program, my guess is that if there is a math course in most of them it consists of something like, “Here’s the Harcourt Brace textbook. Here’s the Saxon textbook. Here’s the Scott Foresman textbook. Here are some tricks for teaching long division.”

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"I will very briefly describe these three methods [sig figs, calculus, and Monte Carlo] and then use them to determine the uncertainty for the volume of the ball above. I will also (for comparison) find the uncertainty in the coefficient of friction for a block sliding down a plane – just because it is different."

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